Dominant H-Eigenvectors of Tensor Kronecker Products Do Not Decouple

Ayush Kulkarni; Charles Colley; David F. Gleich

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arXiv · 2508.19902

Dominant H-Eigenvectors of Tensor Kronecker Products Do Not Decouple

Ayush Kulkarni·Charles Colley·David F. Gleich

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Abstract

We illustrate a counterexample to an open question related to the dominant H-eigenvector of a Kronecker product of tensors. For matrices and Z-eigenvectors of tensors, the dominant eigenvector of a Kronecker product decouples into a product of eigenvectors of the tensors underlying the Kronecker product. This does not occur for H-eigenvectors and indeed, the largest H-eigenvalue can exceed the product of the H-eigenvalues of the component tensors. Beyond this general counterexample, we show this decoupling does hold in the case of diagonal tensors as well as nonnegative tensors.

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Ayush Kulkarni, Charles Colley, David F. Gleich. 2025-08-27. Dominant H-Eigenvectors of Tensor Kronecker Products Do Not Decouple. https://arxiv.org/abs/2508.19902

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